Robust Beamforming Design for Multi-User MISO Full-Duplex SWIPT System With Channel State Information Uncertainty

A multi-user multiple-input single-output simultaneous wireless information and power transfer full-duplex system with imperfect channel state information is considered. Under the assumption that the unknown channel estimation error is within a certain range, the self-interference cannot be suppressed completely at the base station and at the multi-user nodes. The proposed design problem is formulated as maximizing the average harvested energy of multi-user nodes and maintaining the signal-to-interference-plus-noise ratio requirement, which is proved to be non-convex. Utilizing semidefinite relaxation and S-procedure methods, a convex optimization problem of optimal beamforming vector for the multi-antenna transmitter is obtained. Moreover, semidefinite relaxation is proved to be tight by showing the existence of rank-one optimal solutions. Simulation results are presented to verify the robustness and effectiveness of the proposed algorithm compared with the non-robust design.